Question

K= n times n + 9n +1

Answer 1

Answer:

We have that the equation is:

K = n*n + 9n + 1

we want to see if k is prime for all the integer numbers between 1 and 9.

K = n^2 + 9n + 1

lets choose n = 2

k = 2^2 + 9*2 + 1 = 4 + 9*2 + 1 = 21

And we know that 21 = 7*3

so 21 is not prime.

if the equation was:

K = n*(n + 9n + 1)

and again we chose n = 2, we will have that k is a even number (because we will be having 2*something = even number)

So this value of k can not be prime, because 2 is the only even prime number.

Answer 2

k = n(n^2 +9n+1)

expand brackets

k = n^3 + 9n^2 + n

first subsitute 1 as n to see if the result is prime.

k = (1)^3 + 9(1)^2 + 1

k = 1 + 9 + 1

k = 11 (this number is prime)

then substitute 2

k = (2)^3 + 9 (2)^2 + 2

k = 8 + 9 (4) + 2

k = 36 + 10

k = 46 (THIS NUMBER IS NOT PRIME SO MO IS WRONG)